Answer to Question #127716 in Linear Algebra for Sheraz

Question

A company produces two products. Each product requires a certain amount of raw material. Product A requires 3 ponds of the raw material and product B 4 pounds. For any given week, the availability of the raw material is 2,400 pounds. If x equals the number of units produced of product A and Y the number of units of product B:
Determine the equation which states that total raw material used each week equals 2,400 pounds.
Rewrite the equation in slope-intercept form and identify the slope and Y-intercept.
Interpret the values of the slope and Y-intercept.

Answer 1

Let X equals the number of units produced of product A and Y the number of units of product B.

Given Product A requires 3 ponds of the raw material and product B 4 pounds.

Hence, Number of pounds required to produce X units of product A = 3X

and Number of pounds required to produce Y units of product B = 4Y

Hence the equation which states that total raw material used each week equals 2,400 pounds is 3X + 4Y = 2400.

$\implies Y = \frac{2400-3X}{4} \\ \implies Y = - \frac{3}{4} X + 600$ .

Hence, the equation in slope-intercept form is $Y = -\frac{3}{4}X+600$ where slope is $-\frac{3}{4}$ and Y-intercept is 600.

It means 600 units of product B alone is required to produce 2400 pounds.

Since slope is negative, as X increases, Y decreases.